Efficiently Explaining CSPs with Unsatisfiable Subset Optimization

Abstract

We build on a recently proposed method for explaining solutions of constraint satisfaction problems. An explanation here is a sequence of simple inference steps, where the simplicity of an inference step is measured by the number and types of constraints and facts used, and where the sequence explains all logical consequences of the problem. We build on these formal foundations and tackle two emerging questions, namely how to generate explanations that are provably optimal (with respect to the given cost metric) and how to generate them efficiently. To answer these questions, we develop 1) an implicit hitting set algorithm for finding optimal unsatisfiable subsets; 2) a method to reduce multiple calls for (optimal) unsatisfiable subsets to a single call that takes constraints on the subset into account, and 3) a method for re-using relevant information over multiple calls to these algorithms. The method is also applicable to other problems that require finding cost-optimal unsatiable subsets. We specifically show that this approach can be used to effectively find sequences of optimal explanation steps for constraint satisfaction problems like logic grid puzzles.

Sudoku Assistant – an AI-Powered App to Help Solve Pen-and-Paper Sudokus

“…The Thirty-Seventh AAAI Conference on Artificial Intelligence (AAAI-23) learn some solving strategies along the way. For this, we integrated explanations from (Bogaerts, Gamba, and Guns 2021;Gamba, Bogaerts, and Guns 2021).…”

“…1c, highlights which existing digits and constraints can be used to derive that cell's value. The underlying technology relies on a constraint solver to find an Optimal Constrained Unsatisfiable Subset (OCUS) of a derived unsatisfiable formula for (the negation of) each of the empty cells (Bogaerts, Gamba, and Guns 2021;Gamba, Bogaerts, and Guns 2021).…”

“…Scalability Preliminary experiments have shown that generating hints with the out-of-the-box OCUS-algorithm of Gamba, Bogaerts, and Guns (2021) is too slow for an interactive setting. Therefore, we adopt a two-stage approach which works as follows.…”

Tractable Explanations for d-DNNF Classifiers

“…Although recent years have witnessed a growing interest in finding explanations of machine learning (ML) models (Lipton 2018;Guidotti et al 2019;Weld and Bansal 2019;Monroe 2021), explanations have been studied from different perspectives and in different branches of AI at least since the 80s (Shanahan 1989;Falappa, Kern-Isberner, and Simari 2002;Pérez and Uzcátegui 2003), including more recently in constraint programming (Amilhastre, Fargier, and Marquis 2002;Bogaerts et al 2020;Gamba, Bogaerts, and Guns 2021). In the case of ML models, non-heuristic explanations have been studied in recent years (Shih, Choi, and Darwiche 2018;Ignatiev, Narodytska, and Marques-Silva 2019a;Shih, Choi, and Darwiche 2019;Narodytska et al 2019;Ignatiev, Narodytska, and Marques-Silva 2019b,c;Darwiche and Hirth 2020;Ignatiev et al 2020a;Ignatiev 2020;Audemard, Koriche, and Marquis 2020;Marques-Silva et al 2020;Barceló et al 2020;Ignatiev et al 2020b;Izza, Ignatiev, and Marques-Silva 2020;Wäldchen et al 2021;Izza and Marques-Silva 2021;Malfa et al 2021;Ignatiev and Marques-Silva 2021;Cooper and Marques-Silva 2021;Huang et al 2021;Audemard et al 2021;Marques-Silva and Ignatiev 2022;Ignatiev et al 2022;Shrotri et al 2022).…”

Logic-Based Explainability in Machine Learning

“…Although at present ML model explainability of ML models is the most studied theme in the general field of explainability, it is also the case that explainability has been studied in AI for decades [11-13, 96, 103, 104, 113, 250, 276, 278, 292, 293], with a renewed interest in recent years. For example, explanations have recently been studied in AI planning [65,94,95,111,142,194,288,289,291,302], constraint satisfaction and problem solving [54,99,115,135,289], among other examples [290]. Furthermore, there is some agreement that regulations like EU's General Data Protection Regulation (GDPR) [100] effectively impose the obligation of explanations for any sort of algorithmic decision making [129,188].…”